6 ms·

Something I've never understood about 2D/Flatland as a "visual" idea: In the case of this Mar1d, if I'm on the X-axis, and can only see the Y-axis, wouldn't an

• ryanisnan 4y ago
  If the width of a pixel along the Z-axis is arbitrary, and you only see one, no, it would not be 3D. It's still 2D, you just have the ability to more easily see. You gain no new information.
  • cassianoleal 4y ago
    I'm with GP on this one. You say "width of a pixel". That width is a dimension. If that dimension exists, along with X and Y, then it should 3D. And that's when talking about video-games or computer graphics. In the Flatland example, there are no pixels. The characters shouldn't be able to see each other or the structures on their 2D plane at all.
    • Bakary 4y ago
      They can if you see it as some sort of one-bit messaging as opposed to traditional vision
    • bee_rider 4y ago
      Characters in a flat universe would have different sensory organs than us, talking about "sight" seems more like a translation for humans. "Sight" is a highly directional, high-resolution, low-latency sense, the physics of it... I mean the characters might not even understand it, we didn't for the vast majority of human history. All of physics would have to be different anyway, down to really fundamental stuff like how quantities which spread from a source radially operate, since we'd be looking at perimeters rather than surface areas.
    • jakelazaroff 4y ago
      Don't think of the "width of a pixel" as what you'd see from the perspective of that 2D plane — think of it as a 2D projection of a 1D space.
    • fnordpiglet 4y ago
      No, it’s not. A dimension requires freedom to be parameterized and independence from other dimensions. In this example “Y” is invariantly defined as 1. Similarly a level surface defines a dimension to a fixed value and provides an n-1 dimensional view of a n dimensional view. Mapping this to a level surface you declare Y=1 and only X is varying. Y has scale but no dimensionality due to its lack of freedom.
• bee_rider 4y ago
  I think we have to imagine 2D Mario, as a being which lives in a 2D world, has his "sight" via an organ which has evolved differently from a human eye. So, the the viewport with a single wide pixel is really just an appropriate visualization for us 3D beings.
• d23 4y ago
  I think you're right, and while I think something simple like fading in and out the elements based on distance would be reasonable (since the game would be unplayable otherwise, as you'd be able to see the entire level), the choice they appear to have made (something non-orthographic) seems to essentially be fully encoding the extra dimension. Otherwise, I can't see how the goomba would appear to get bigger as it gets closer to mario.
• Bakary 4y ago
  In a properly 2D universe, there would be the equivalent of some sort of planck length that is essentially the only length. The equivalent of a string of one-bit messages that shift around. We chose to visualize it through something that has width because we are unable to properly understand the alternative.
• fnordpiglet 4y ago
  No. To be a dimension there needs to be freedom. In this case the Y is quantized at one pixel and there’s no independent parameter in that direction, just an invariant quantum.
• chc 4y ago
  I think you're imagining a projection of a 2D world into three dimensions and correctly observing that it's three-dimensional. Imagine a 2D world with two squares and a circle. One of the squares pushes the circle and it rolls into the other square, impacting it. This is all plausible in a purely 2D setting, right? Assuming that these objects can't take up the same 2D space, it makes sense that the square would be impacted by the circle. This is how vision works — photons bounce around and our eyes sense them. There wouldn't actually be any Z-axis to what you're seeing, you'd just be registering 2D photon-equivalents moving in two dimensions. But in order to represent it as something our brains can recognize as "seeing," we have to project the input into some non-zero dimension. A different representation could emphasize this point better. You could have this same basic game, but instead of first-person, have it be third-person but with actual vision simulation, so that you only see the parts of objects that Mario would see and everything else is simply absent.
• EmilyHughes 4y ago
  Correct. That's why this game is 3D and not 1D.
• babypuncher 4y ago
  It's basically a 2D game but they replaced the width dimension with depth. Wolfenstein 1-D [1] is a true 1-dimensional game. The game is represented by a single straight line of pixels, and player movement is restricted to a single axis. 1: https://en.wikipedia.org/wiki/Wolfenstein_1-D https://en.wikipedia.org/wiki/Wolfenstein_1-D
• tomxor 4y ago
  Yes, it wouldn't be 3D, but what you are alluding to is projection (X onto Y, or more generally instead of X which would be orthogonal only, a 1D plane of any orientation - AKA line segment) ultimately you are still looking at a 1D image, but it has a 2D shape projected onto it that changes depending on both your orientation and position, so that you can perceive part of the 2D shape's surface as you move. And this would be more physically correct than either Mario or Mar1D. The generalisation, starting in 3D, is that you can project the surface of a 3D object onto a 2D plane (which is how we see)... we get a little bit more by gauging depth through stereo separation but ultimately we only get to see one 3D projection onto a 2D plane at any point in time, i.e the entire 3D surface is not accessible, we can't see behind it, or inside it, and the perception of 3D is constructed in our mind from a combination of general learned/evolved intuition of 3D space and shape and temporal samples for a particular scenario e.g looking around the object from different angles. Projection can extend to higher and lower dimensions, e.g in 4D space the surface of a 4D object can be projected onto a 3D "plane"; and as you are suggesting, for 2D space you can project a 2D object onto a 1D plane. The projection changing depending on the orientation and position of either the shape or eye/camera. Normal 2D game rendering doesn't really make any physical sense as a projection unless you consider them to be a narrow 3D world (consider the fact that you can see the entire surface of a square and inside of the square, but Mario the character cannot possibly see this, only a small part of the surface). But this is all based on a "projection" with the assumption of a lot of opacity... if each particle received from the projection also contained accurate enough depth information and was a vector of all depths traversed for some limit, then full 3D could be perceived in a single 2D projection within a 3D world i.e if you could see "through" objects while still being able to sample each depth.
  • couchand 4y ago
    Your last comment reminds me of being in thick fog, where distances can be easily estimated by gauging how obscured the object is.
• derefr 4y ago
  A thing photographers / image-effects people think about a lot: pixels aren't little squares; they're sample points. If you've ever played around with graphics-rendering — UV coordinate sampling, convolution, etc — then you know that you can think of a (2D) raster image as really being a grid of samples of what color you get when you look at the UV coordinate represented by the center of that grid-point on some underlying hypothetical continuous texture. Which is to say: if you have a pixel-art image (i.e. one created at pixel scale, pixel by pixel, rather than created with continuous-art techniques and then scaled down), and you want to scale it up "conservatively", without making up any information that doesn't already exist in the image — then the right way to do that isn't to blow up the pixels themselves, nearest-neighbour style (as if the hypothetical underlying texture is a tessellation of infinitely-sharply-bounded little squares); but nor is it to stretch the image with bilinear/cubic/etc. resampling (as if the hypothetical underlying texture is a continuous blend from the color at the center of each sample into its neighbours.) Really, the conservative approach to enlarging a pixel-art image, is to throw your hands up and give up — because you actually don't have the information for what occupies any UV coordinate of the underlying hypothetical continuous texture, other than the exact center-point of each grid square, where the pixel-art pixel sample is located. A pixel-art image, created from scratch as pixels, only really tells you what's at the exact center point of each grid-square. Every other possible sample-point in each grid-square is left undefined. If you picture an infinitely-small dot in the center of each grid-square, with the rest left "empty", that's the data you have about the "underlying image", from seeing a pixel-art image. Anything beyond that is "compressed sensing" — an inference, not a logical deduction. But to directly address your point: you see pixels, because that's how the game has to be rendered — as a 2D extrusion — for it to show up on a screen for you to see. But in concept, the game is giving you a one-dimensional array of sample-points — a sampling of an underlying hypothetical one-dimensional continuous texture.
  • Veedrac 4y ago
    Pixels are very much and in very many cases much more a square than a sample. Cameras integrate lightfall over an area, and though consumer formats munge that data, they surely do not do so in a way that is best approximated by a zero-width point sample. Pixels on most modern displays, albeit not those from the era of the famous 1995 paper, have especially at low resolution visible squareness; not as squares precisely per se, but certainly such that a single-pixel diagonal has an overt XY-aligned jaggedness. GPUs integrate colors over square volumes, to display logical pixels, or rather at least aspire to, with sufficient multisampling or that that approximates it. And then this especially is so for pixel art, whose modern aesthetic assumed the squareness of pixels not as an unfortunate limitation to be worked around, but as a defining and visually appealing characteristic. Pixel art for CRTs and pixel art for (or reinterpreted through the lens of) scaled display on LCDs are fundamentally different visual targets and assumptions on one need not naively apply to the other. And even art made for CRTs often does not truly assume point samples, hence why they often look better through CRT reconstruction filters rather than more idealized mathematical ones.
• LeifCarrotson 4y ago
  The Z axis can be imagined to be infinitesimally narrow. There's no information in the stretching of the Z axis, so you can make that single color of data in the as visible as you like without adding any information. Our eyes see in two dimensions, so a Mar1d world with a Z axis one Plank length wide would still have the same colors, but it's impossible to see.
• dusted 4y ago
  Another perspective on this is.. When we're rendering a 3D environment on a 2D plane, we're projecting it "down", so that we can perceive it. When we're rendering a 2D environment on a 2D plane, are we doing nothing to to ? Maybe, but the 2D environment we've constructed to begin with is probably inspired from our native 3D thinking. But when we're rendering a 1D environment on a 2D plane, which we need to do to perceive it, because we don't have a visual organ for perceiving 1D environments of the kinds constructed in "native 2D thinking".. So we're projecting "up", adding data to convey a representation of the environment that we can perceive, not as it "is".